Surface Realization with the Intersection Segment Functional
Hougardy, Stefan ; Lutz, Frank H. ; Zelke, Mariano
Experiment. Math., Tome 19 (2010) no. 1, p. 79-92 / Harvested from Project Euclid
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Deciding realizability of a given polyhedral map on a (compact, connected) surface belongs to the hard problems in discrete geometry from the theoretical, algorithmic, and practical points of view. ¶ In this paper, we present a heuristic algorithm for the realization of simplicial maps, based on the intersection segment functional. This heuristic was used to find geometric realizations in ${\mathbb R}^3$ for all vertex-minimal triangulations of the orientable surfaces of genera $g=3$ and $g=4$. Moreover, for the first time, examples of simplicial polyhedra in ${\mathbb R}^3$ of genus 5 with 12 vertices have been obtained.
Publié le : 2010-05-15
Classification:  Triangulated surface,  polyhedral realization,  intersection segment functional,  52B70,  57Q15 
@article{1268404804,
     author = {Hougardy, Stefan and Lutz, Frank H. and Zelke, Mariano},
     title = {Surface Realization with the Intersection Segment Functional},
     journal = {Experiment. Math.},
     volume = {19},
     number = {1},
     year = {2010},
     pages = { 79-92},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1268404804}
}

Hougardy, Stefan; Lutz, Frank H.; Zelke, Mariano. Surface Realization with the Intersection Segment Functional. Experiment. Math., Tome 19 (2010) no. 1, pp.  79-92. http://gdmltest.u-ga.fr/item/1268404804/